Subgroups — #43247768

Order 28352.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₄₄₃	C₂	1	1	yes	maximal, characteristic
2	Dic₄₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	(C₂×D₄₄₃)⋊C₈	C₂	1	2	yes	maximal
4	C₄×C₄₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₄₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄₄₃⋊C₈	C₂²	1	2	yes	—
10	C₄×Dic₄₄₃	C₄	1	1	yes	characteristic
11	C₄×Dic₄₄₃	C₄	1	1	yes	characteristic
12	C₄×Dic₄₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₄₄₃	C₂²	1	2	yes	—
14	C₄²×C₄₄₃	C₂²	1	1	yes	characteristic
15	C₂²×D₄₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₄₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₄₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₄₄₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₄₄₃	—	2	2	no	—
20	C₄×D₄₄₃	—	2	2	no	—
21	C₄×D₄₄₃	C₈	1	4	yes	complemented
22	C₄₄₃⋊C₈	—	2	2	no	—
23	C₂×C₄×C₄₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₄₃	C₂³	1	1	yes	characteristic
26	C₈×C₄₄₃	—	2	2	no	—
27	C₂²×C₄₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₄₃	—	2	1	no	—
29	C₂×D₄₄₃	—	2	1	no	—
30	C₂×D₄₄₃	C₂×C₈	1	2	yes	—
31	C₄×C₄₄₃	C₂×C₈	1	2	yes	—
32	C₄×C₄₄₃	M₁₆	1	2	yes	—
33	C₄×C₄₄₃	#41	1	2	yes	—
34	Dic₄₄₃	—	2	1	no	—
35	Dic₄₄₃	—	2	1	no	—
36	Dic₄₄₃	C₂×C₈	1	2	yes	—
37	C₂×C₄₄₃	#117	1	1	yes	characteristic
38	C₂×C₄₄₃	C₂²×C₈	1	1	yes	characteristic
39	C₂×C₄₄₃	C₂×M₁₆	1	1	yes	characteristic
40	D₄₄₃	—	2	2	no	—
41	C₄₄₃	#431	1	1	yes	characteristic, complemented, Sylow
42	#431	—	443	1	no	maximal, Sylow
43	C₂×C₄²	—	443	1	no	—
44	C₄⋊C₈	—	443	2	no	—
45	C₂²⋊C₈	—	443	2	no	—
46	C₄×C₈	—	443	1	no	—
47	C₄×C₈	D₄₄₃	1	1	yes	characteristic, complemented
48	C₂²×C₄	—	443	1	no	—
49	C₂²×C₄	—	443	1	no	—
50	C₂²×C₄	—	443	1	no	—
51	C₂×C₈	—	443	2	no	—
52	C₂×C₈	C₂×D₄₄₃	1	2	yes	—
53	C₄²	—	443	1	no	—
54	C₄²	—	443	1	no	—
55	C₄²	—	443	1	no	—
56	C₄²	C₂×D₄₄₃	1	1	yes	characteristic
57	C₂³	—	443	1	no	—
58	C₂×C₄	—	886	2	no	—
59	C₂×C₄	—	886	2	no	—
60	C₂×C₄	—	443	1	no	—
61	C₂×C₄	—	443	1	no	—
62	C₂×C₄	—	443	1	no	—
63	C₂×C₄	—	443	4	no	—
64	C₂×C₄	C₄×D₄₄₃	1	1	yes	characteristic
65	C₂×C₄	C₄×D₄₄₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₄₄₃	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	886	2	no	—
69	C₂²	—	886	1	no	—
70	C₂²	—	886	1	no	—
71	C₂²	—	443	2	no	—
72	C₂²	C₂×C₄×D₄₄₃	1	1	yes	characteristic
73	C₄	—	886	1	no	—
74	C₄	—	886	1	no	—
75	C₄	—	443	2	no	—
76	C₄	C₈×D₄₄₃	1	2	yes	—
77	C₄	#20296770	1	2	yes	—
78	C₄	#20296787	1	2	yes	—
79	C₂	—	886	2	no	—
80	C₂	#28381843	1	1	yes	characteristic
81	C₂	C₂×C₈×D₄₄₃	1	1	yes	characteristic
82	C₂	C₂×#20296770	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₄₄₃
commutator	C₂×C₄₄₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₄₄₃
Fitting	C₄×C₈×C₄₄₃	C₂
socle	C₂²×C₄₄₃	C₂²×C₄
prime radical	C₂²×D₄₄₃	C₂×C₄
cosocle	C₂×C₄×C₄₄₃	C₂³
hypercenter	C₄×C₈	D₄₄₃
hypocenter	C₄₄₃	#431
LCS	G ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. Dic₄₄₃⋊C₈	C₂	semidirect
4. C₄×C₄₄₃⋊C₈	C₂	semidirect
5. C₄×C₈×C₄₄₃	C₂	semidirect
21. C₄×D₄₄₃	C₈	semidirect
41. C₄₄₃	#431	semidirect
47. C₄×C₈	D₄₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄²×D₄₄₃	2
Dic₄₄₃⋊C₈	2
(C₂×D₄₄₃)⋊C₈	2
C₄×C₄₄₃⋊C₈	2
C₄×C₈×C₄₄₃	2
#431	443